Question: Evaluate the definite integral. $\int^{7}_{-14}7e^x\,dx = $ Choose 1 answer: Choose 1 answer: (Choice A) A $e^{7}+\dfrac{e^{-14}}{2}$ (Choice B) B $7e^{7}-7e^{-14}$ (Choice C) C $49e^{7}+98e^{-14}$ (Choice D) D None of the above
Solution: First, use the exponent rule: $\begin{aligned}\int^{7}_{-14}7e^x\,dx =~7e^x\Bigg|^{7}_{{-14}}\end{aligned}$ Second, plug in the limits of integration: $(7e^{{7}})-(7e^{{-14}}) = 7(e^{7}-e^{-14})$. The answer: $\int^{7}_{-14}7e^x\,dx~=~7(e^{7}-e^{-14})$